The circuit-relation ideal conjecture for 3-connected matroid extensions

Let ${\mathbb{P}}$ be a partial field, let $M$ be a 3-connected ${\mathbb{P}}$-representable matroid, and let $N=M{-} e$ be a 3-connected deletion that settles $M$. Let $I_{N,M}$ be the ideal describing the quotient from the representation ring of $N$ to that of $M$, and let $\operatorname{Cr}(N)$ denote the relevant set of cross-ratios of $N$. Circuit-relation ideal conjecture. If $N=M{-} e$, $N$ and $M$ are 3-connected, and $N$ settles $M$, then $I_{N,M}$ is an ideal generated by relations $p-q$, where $p,q\in\operatorname{Cr}(N)$.

This conjecture proposes that the constraints imposed by extending a settled 3-connected matroid are generated by pairwise relations between cross-ratios of the smaller matroid. The source gives no evidence that the claim has been resolved.